Group #19136477 — subgroups

Subgroups — #19136477

Order 5504.

146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583331	C₂	1	1	yes	maximal, characteristic
2	#14583017	C₂	1	2	yes	maximal, complemented
3	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582707	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	C₂²	1	2	yes	—
7	#13063331	—	2	2	no	—
8	Dic₃₄₄	C₄	1	1	yes	characteristic, complemented
9	#13063270	C₄	1	2	yes	complemented
10	D₆₈₈	C₄	1	1	yes	characteristic, complemented
11	#13063261	C₂²	1	2	yes	—
12	#13063253	—	2	2	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	#10621898	—	2	2	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	#10621877	—	2	2	no	—
21	Dic₁₇₂	C₂×C₄	1	2	yes	—
22	D₃₄₄	C₂×C₄	1	2	yes	—
23	#10621873	—	2	2	no	—
24	#10621872	—	4	2	no	—
25	C₈×D₄₃	—	4	2	no	—
26	C₁₆×C₄₃	—	2	1	no	—
27	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₄₃	—	4	2	no	—
32	D₁₇₂	—	2	2	no	—
33	C₄×D₄₃	—	4	2	no	—
34	Dic₈₆	—	2	2	no	—
35	C₈×C₄₃	D₈	1	1	yes	characteristic
36	C₈×C₄₃	D₈	1	1	yes	characteristic
37	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₄₃	#41	1	1	yes	characteristic
39	C₄₃⋊C₈	—	4	2	no	—
40	C₂²×C₄₃	#135	1	1	yes	characteristic
41	C₂×D₄₃	—	4	2	no	—
42	C₄×C₄₃	—	2	2	no	—
43	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
44	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
45	Dic₄₃	—	4	2	no	—
46	#2178	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	—	2	1	no	—
48	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
49	D₄₃	—	8	2	no	—
50	#508	—	43	1	no	—
51	#443	—	43	2	no	—
52	#368	—	43	1	no	—
53	#359	—	43	2	no	—
54	C₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
55	C₄₃	#2178	1	1	yes	characteristic, complemented, Sylow
56	#135	—	43	2	no	—
57	#131	—	86	2	no	—
58	Q₃₂	—	43	1	no	—
59	SD₃₂	—	43	2	no	—
60	D₁₆	—	43	1	no	—
61	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
62	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
63	#108	—	43	2	no	—
64	#104	—	86	2	no	—
65	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
66	#41	—	86	2	no	—
67	Q₁₆	—	43	2	no	—
68	SD₁₆	—	86	2	no	—
69	D₈	—	43	2	no	—
70	M₁₆	—	86	2	no	—
71	M₁₆	—	172	2	no	—
72	C₂×C₈	—	172	2	no	—
73	C₂×C₈	D₁₇₂	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
75	C₄²	D₁₇₂	1	1	yes	characteristic
76	C₁₆	—	2	1	no	—
77	C₁₆	C₄×D₄₃	1	1	yes	characteristic
78	C₁₆	C₄×D₄₃	1	1	yes	characteristic
79	Q₈	—	86	2	no	—
80	D₄	—	86	2	no	—
81	D₄	—	172	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	172	2	no	—
84	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
85	C₈	—	172	2	no	—
86	C₈	D₃₄₄	1	1	yes	characteristic
87	C₈	D₃₄₄	1	1	yes	characteristic
88	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
89	C₈	#10621898	1	1	yes	characteristic
90	C₂²	—	172	2	no	—
91	C₂²	#13063347	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	172	2	no	—
94	C₄	C₄×D₁₇₂	1	1	yes	characteristic
95	C₄	C₂×D₃₄₄	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	344	2	no	—
98	C₂	C₄×D₃₄₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583331

C₂

yes

maximal, characteristic

#14583017

C₂

yes

maximal, complemented

#14582729

C₂

yes

maximal, characteristic, complemented

#14582707

C₂

yes

maximal, complemented

C₄×C₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

—

#13063331

—

Dic₃₄₄

C₄

yes

characteristic, complemented

#13063270

C₄

yes

complemented

D₆₈₈

C₄

yes

characteristic, complemented

#13063261

C₂²

yes

—

#13063253

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

#10621898

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

#10621877

—

Dic₁₇₂

C₂×C₄

yes

—

D₃₄₄

C₂×C₄

yes

—

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

#135

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

#2178

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×D₈

yes

characteristic

D₄₃

—

—

—

—

—

C₄×C₁₆

D₄₃

yes

characteristic, complemented

C₄₃

#2178

yes

characteristic, complemented, Sylow

#135

—

#131

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₁₆

—

C₁₆

C₄×D₄₃

yes

characteristic

C₁₆

C₄×D₄₃

yes

characteristic

Q₈

—

D₄

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₈

—

172

—

C₈

D₃₄₄

yes

characteristic

C₈

D₃₄₄

yes

characteristic

C₈

C₂×C₄×D₄₃

yes

characteristic

C₈

#10621898

yes

characteristic

C₂²

—

172

—

C₂²

#13063347

yes

characteristic

C₄

—

C₄

—

172

—

C₄

C₄×D₁₇₂

yes

characteristic

C₄

C₂×D₃₄₄

yes

characteristic

C₂

—

C₂

—

344

—

C₂

C₄×D₃₄₄

yes

characteristic

	subgroup	G/H
center	C₈	D₃₄₄
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂×C₄₃	C₄×D₈
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#2178
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₈

D₃₄₄

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×C₁₆×C₄₃

C₂

socle

C₂×C₄₃

C₄×D₈

hypercenter

C₄×C₁₆

D₄₃

hypocenter

C₄₃

#2178

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #14583017	C₂	semidirect
3. #14582729	C₂	semidirect
4. #14582707	C₂	semidirect
5. C₄×C₁₆×C₄₃	C₂	semidirect
8. Dic₃₄₄	C₄	semidirect
9. #13063270	C₄	semidirect
10. D₆₈₈	C₄	semidirect
54. C₄×C₁₆	D₄₃	semidirect
55. C₄₃	#2178	semidirect

H ≅ G/N

type

2. #14583017

C₂

semidirect

3. #14582729

C₂

semidirect

4. #14582707

C₂

semidirect

5. C₄×C₁₆×C₄₃

C₂

semidirect

8. Dic₃₄₄

C₄

semidirect

9. #13063270

C₄

semidirect

10. D₆₈₈

C₄

semidirect

54. C₄×C₁₆

D₄₃

semidirect

55. C₄₃

#2178

semidirect

Subgroups — #19136477

Conjugacy classes of subgroups

Complements